On the regularization of sequences and associated weight functions
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929437091561472 |
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| author | Schindl, Gerhard |
| author_facet | Schindl, Gerhard |
| contents | We revisit and generalize the geometric procedure of regularizing a sequence of real numbers with respect to a so-called regularizing function. This approach was studied by S. Mandelbrojt and becomes useful and necessary when working with corresponding classes of ultradifferentiable functions defined via weight sequences and analogous weighted spaces. In this note we also study non-standard situations for the construction yielding the (log-)convex minorant of a sequence and allow a "blow-up" for the regularizing function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_07902 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the regularization of sequences and associated weight functions Schindl, Gerhard Classical Analysis and ODEs 26A12, 26A48, 26A51 We revisit and generalize the geometric procedure of regularizing a sequence of real numbers with respect to a so-called regularizing function. This approach was studied by S. Mandelbrojt and becomes useful and necessary when working with corresponding classes of ultradifferentiable functions defined via weight sequences and analogous weighted spaces. In this note we also study non-standard situations for the construction yielding the (log-)convex minorant of a sequence and allow a "blow-up" for the regularizing function. |
| title | On the regularization of sequences and associated weight functions |
| topic | Classical Analysis and ODEs 26A12, 26A48, 26A51 |
| url | https://arxiv.org/abs/2307.07902 |